A bijection maps LU orbits of AME states (n even) to orbits of ((n-1,D,n/2))_D codes, with the 4-qutrit AME state and ((3,3,2))_3 code both unique up to LU and their symmetry/transversal groups explicitly generated via Vinberg theory.
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Transversal gates of the ((3,3,2)) qutrit code and local symmetries of the absolutely maximally entangled state of four qutrits
A bijection maps LU orbits of AME states (n even) to orbits of ((n-1,D,n/2))_D codes, with the 4-qutrit AME state and ((3,3,2))_3 code both unique up to LU and their symmetry/transversal groups explicitly generated via Vinberg theory.